a single phase photovoltaic inverter control for grid

Sadhana Vol. 41, No. 1, January 2016, pp. 15–30 c© Indian Academy of Sciences

A single phase photovoltaic inverter control for grid connected system

AUROBINDA PANDA∗, M K PATHAK and S P SRIVASTAVA

Department of Electrical Engineering, Indian Institute of Technology Roorkee, Roorkee,

Uttrakhand 247667, India

e-mail: [email protected]

MS received 15 October 2014; revised 2 June 2015; accepted 16 October 2015

Abstract. This paper presents a control scheme for single phase grid connected photovoltaic (PV) system

operating under both grid connected and isolated grid mode. The control techniques include voltage and current

control of grid-tie PV inverter. During grid connected mode, grid controls the amplitude and frequency of the

PV inverter output voltage, and the inverter operates in a current controlled mode. The current controller for grid

connected mode fulfills two requirements – namely, (i) during light load condition the excess energy generated

from the PV inverter is fed to the grid and (ii) during an overload condition or in case of unfavorable atmospheric

conditions the load demand is met by both PV inverter and the grid. In order to synchronize the PV inverter with

the grid a dual transport delay based phase locked loop (PLL) is used. On the other hand, during isolated grid

operation the PV inverter operates in voltage-controlled mode to maintain a constant amplitude and frequency of

the voltage across the load. For the optimum use of the PV module, a modified P&O based maximum power point

tracking (MPPT) controller is used which enables the maximum power extraction under varying irradiation and

temperature conditions. The validity of the proposed system is verified through simulation as well as hardware

implementation.

Keywords. Current controller; MPPT; photovoltaic; PLL; PV inverter; voltage controller.

1. Introduction

The principal source of electrical energy is the hydrocar-

bon based fossil fuel. CO2 emission from fossil fuel based

power plants is a major cause of global warming. In addi-

tion, the availability of such energy resources is very limited

for the future consumption [1]. These are the reasons, which

attract many researchers to work in the area of renewable

energy. Among all the available renewable energy sources,

solar photovoltaic (PV) system has several advantages such

as clean energy and potential to provide sustainable electric-

ity to remote areas [1, 2]. They can be installed in residential

or commercial complexes to meet partial/full load demand.

In case the power generated by PV system is more than the

load demand, the excess power can be fed to the grid [3].

However, the major constraints in the development of a grid

connected PV system are – cost of PV module and inter-

facing of PV inverter with the grid [4, 5]. Because of these

challenges, it is necessary to use the energy of PV module

optimally. Moreover, interfacing of PV system with the grid

requires a number of controllers to handle many issues at the

same time. Therefore, this paper presents all the controllers

that are required for the development of a simpler form

of grid connected PV system. Starting from the generation

∗For correspondence

side, an MPPT controller is used to maximize the utiliza-

tion of solar power for a given insolation and temperature

condition [6, 7]. In the instantaneous maximum power point

(MPP) tracking (MPPT), the PV module is operated in con-

junction with a DC–DC converter. Several MPPT schemes

have been proposed in the literature [7]. Some of the popular

MPPT schemes are perturbed and observe (P&O), incre-

mental conductance (IC), open circuit voltage, short circuit

current, etc. [7, 8]. The IC method is based on the fact that,

the slope of the power curve is zero at MPP, negative on

the right and positive on the left of the MPP. In [9], the

author claims that this method is prone to failure in case

of large change in atmospheric conditions. The fractional

short circuit method of MPPT is discussed in [10]. However,

as this method approximates a constant ratio, its accuracy

cannot be guaranteed under varying weather conditions. To

overcome the above-mentioned drawbacks, several artificial

intelligence based MPPT controllers have been proposed

[11, 12]. But these methods also have drawbacks such as,

the requirement of large data storage and extensive compu-

tation. Among all the available MPPT techniques, the P&O

is the most widely used MPPT scheme due to its simplicity.

In [13], a review on P&O techniques has been presented. In

this method the operating point oscillates around the MPP

giving rise to wastage of energy. These oscillations can be

minimized by reducing the fixed perturbation step size, but

15

16 Aurobinda Panda et al

then it takes more time to reach MPP. To overcome this

conflicting situation, a modified P&O MPPT algorithm with

variable step size is proposed. As the PV module output is

a DC, power electronic devices are required to convert this

DC power into AC power for grid interface [14], and for

this DC–AC inverter is required. The synchronization of PV

inverter with the grid is done with the help of a phase locked

loop (PLL) [1, 15]. The main task of the PLL is to provide a

unity power factor operation which includes synchronization

of the inverter output current with the grid voltage [16–18].

There has been an increasing interest in PLL topologies

for distributed generation system [14, 15]. It is a grid volt-

age phase detection structure which requires orthogonal

voltages. In single-phase PLL, accurate and fast phase esti-

mation can be obtained by processing a signal in phase with

the grid voltage (original signal) and another one which is

90◦ phase shifted from it [19, 20]. The PLL, which generates

orthogonal signals by delaying the original signal, is called

a transport-delay PLL (TDPLL) [21]. This type of PLL is

simple and its transient response is fast and smooth among

all available PLL methods [22]. The other methods for

generating orthogonal voltages are Hilbert transformation,

Park transformation, etc. All these methods have shortcom-

ings such as high complexity, nonlinearity and have slower

response than TDPLL [23]. Artificial intelligence controller

based PLL has also been proposed, however they are rel-

atively more complex and are not suitable for control of

PV inverters [24]. This paper presents a single-phase PLL

structure, which generates the orthogonal signal by using

transport delay. The main drawback of conventional TDPLL

is its sensitivity to the grid frequency changes, since the

delay is determined assuming constant frequency. Here, a

modified TDPLL is suggested which uses two delay blocks

to make TDPLL robust against frequency variation. In addi-

tion to MPPT and grid synchronization controller, the other

controllers required for a grid connected PV system are DC-

link voltage controller, current controller and PV inverter

voltage controller. Many research efforts have been going on

in the area of grid interfaced PV system [25–27]. Current

controllers are used to regulate the current, so that it follows

the reference current, whereas voltage controller is used to

control the PV inverter output voltage and frequency dur-

ing isolated grid operation. There are several techniques to

control the current and voltage such as PI controllers, hys-

teresis controllers, predictive controllers and sliding mode

controllers. In [28], a hysteresis controller is proposed which

is having fast response but operates at varying switching

frequency. The predictive controller [29] overcomes the lim-

itation of hysteresis controllers as it has constant switching

frequency but it cannot properly match with change in atmo-

spheric conditions. An analytical method is proposed in

[30] to determine the control parameters in steady state, but

this method cannot be implemented easily during transients,

which are natural in PV systems. This paper uses PI con-

trollers [31, 33] for both current and voltage control of the

PV inverter system.

2. Grid connected rooftop photovoltaic system

Figure 1 shows the schematic diagram of a grid connected

photovoltaic system. It includes two PV module, two DC–

DC converters, inverter, controllers and the grid. The DC–

DC converters along with an MPPT controller are used to

extract the maximum power from each PV module. DC to

AC converter is used to interface the PV system to the grid.

Figure 1. Schematic diagram of a 1−φ grid connected PV system [31].

A 1-φ PV inverter control for grid connected system 17

V

IRS

RShIdIPV

Figure 2. Equivalent model of PV cell [32].

Phase locked loop (PLL) controller is used for the synchro-

nization of PV inverter with the grid. During grid connected

mode, inverter operates in a current controlled mode with

the help of a current controller. While, in grid isolated mode,

a voltage controller is used to maintain the required terminal

voltage and frequency at a desired level.

3. PV modeling and parameter estimation

In order to analyze the grid connected PV system, it is

essential to model the PV module connected to the system

by using data available from the manufacturer’s datasheet.

However, some of the parameters required for the model-

ing of PV module are not given in the datasheet. All these

parameters are estimated from datasheet values and then

used in modeling. The equivalent circuit of a practical PV

cell is shown in figure 2.

The characteristic equation of a PV cell is expressed as

[4],

I = IPV − I0

[

exp

(V + IRS

NsVt

)

− 1

]

− V + IRS

RSh

. (1)

The available parameters of the PV module and the param-

eters to be estimated are tabulated in table 1. The procedure

for the parameter estimation is given below:

Since the exponential term in Eq. (1) is much larger than

1, it can be re-written as

I = IPV − I0

[

exp

(V + IRS

NsVt

)]

− V + IRS

RSh

. (2)

Substituting three significant-points of the I − V charac-

teristic of PV module, namely: the short-circuit point (0,

ISC), the maximum power point (VMPP , IMPP ), and the

open-circuit point (VOC, 0) in Eq. (2) gives

ISC = IPV − I0

[

exp

(ISCRS

NsVt

)]

− 0 + ISCRS

RSh

(3)

IMPP = IPV − I0

[

exp

(VMPP + IMPP RS

NsVt

)]

−VMPP + IMPP RS

RSh

(4)

IPV = I0

[

exp

(VOC

NSVt

)]

+ VOC

RSh

. (5)

At MPP, the derivative of power with respect to voltage is

zero [32].dP

dV

∣∣∣∣MPP

= 0. (6)

Similarly, at short circuit condition [32],

dI

dV

∣∣∣∣I=ISC

= − 1

RSh

. (7)

From Eqs. (5) and (3), I0 can be expressed as

I0 =(

ISC − VOC − ISCRS

RSh

)

exp

(−VOC

NsVt

)

. (8)

Substituting Eq. (8) in Eq. (5)

IPV = ISC + ISCRS

RSh

(9)

From Eq. (4) and Eq. (9),

IMPP =[

ISC − VMPP + IMPP RS − ISCRS

RSh

]

−[(

ISC − VOC − ISCRS

RSh

)

e

(VMPP +IMPP RS−VOC

NsVt

)]

.

(10)

The transcendental equation (10) still contains three

unknown parameters: RS , RSh and Vt . Therefore, for the

estimation of all these parameters additional equations are

required which are derived below.

The rate of change of power with respect to voltage at

MPP can be written as

dP

dV

∣∣∣∣MPP

= IMPP +VMPP

∂∂VMPP

f (V, I )

1 − ∂∂IMPP

f (V, I ). (11)

Table 1. Available and estimated PV module parameters.

Parameters available in datasheet at STCsa Parameters to be estimated

IMPP , VMPP , KI , KV , PMAX,e, VOC and ISC a, RS , RSh, IPV and I0

aStandard test conditions (STCs) of temperature (25◦C) and solar irradiation (1000 W/m2).


where

Table 2. Datasheet’s and estimated parameters of PV module.

Available datasheet parameters of PV module (ProductId.120 H24, Maharishi Solar, India)

ISC VOC VMPP IMPP PMPP KV KI

3.82 A 44.11 V 35.62 V 3.595 A 128.1 W −2.10 mV/cell/◦ c 15 μ A/cell/◦ c

Estimated parameters

IPV I0 RS Rsh A

3.82 A 0.102 μ A 0.31 � 600 � 1.2

∂f (V, I )

∂VMPP

=(VOC − ISC (RS + RSh)) exp

(VMPP + IMPP RS − VOC

NsVt

)

NsVtRSH

− 1

RSh

(12)

∂f (V, I )

∂IMPP

=(VOC − ISC (RS + RSh)) exp


NsVt

)

NsVtRSh

RS − RS

RSh

. (13)

By substituting Eq. (12) and Eq. (13) in Eq. (11), we have

dP

dV

∣∣∣∣MPP

= IMPP + VMPP

(VOC − ISC (RS + RSh)) exp


NsVt

)

NsVtRSh

− 1

RSh

1 +lRS (ISC (RS + RSh) − VOC) exp


NsVt

)

NsVtRSh

+ RS

RSh

= 0. (14)

Similarly, substituting Eq. (12) and Eq. (13) in Eq. (7), we have

dI

dV

∣∣∣∣(0,ISC )

= − 1

RSh

=

l (VOC − ISC (RS + RSh)) exp

(ISCRS − VOC

NsVt

)

NsVtRSH

− 1

Rsh

1 +(ISC (RS + RSh) − VOC) exp

(ISCRS − VOC

NsVt

)

NsVtRSh

+ RS

RSh

. (15)

Finally, five Eqs. (8), (9), (10), (14) and (15) are to be

solved to calculate five unknown parameters. It is seen that,

(10), (14) and (15) are transcendental in nature. Further,

these three equations are completely independent of IPV

and I0 hence, the numerical method problem reduces to the

determination of three unknowns from three equations: Vt ,

RS and RSh, which can be solved by using Gauss–Seidel

method and then these values are used to obtain the value of

I0 and then IPV from Eq. (8) and (9) respectively. A case

study to find the parameters of the PV module using above

equations is carried out while using a PV module from the

manufacturer, Maharishi Solar, India (http://www.mahari

maharishisolar.com/),. The values provided on the datasheet

are tabulated in table 2 and are followed by the values of the

estimated parameters.

4. Control strategy

Following controllers are used for the development of a

single-phase grid connected PV system:

(1) Maximum power point tracking controller

(2) Grid synchronization controller

(3) PV inverter controllerThe detailed description on each controller is given one by

one in the following subsections:

4.1 Maximum power point tracking control

A DC–DC converter (step up/ step down) serves the pur-

pose of extracting maximum power from the PV module. By


Figure 3. Flow chart for the MPPT control of PV module.

changing the duty cycle the load impedance as seen by the

source is varied and matched at the point of the peak power

with the source [6]. The perturb and observe (P&O) method

is used here. It is an iterative method for obtaining MPP.

It measures the PV array characteristics, and then perturbs

the operating point of PV module to obtain the change in

direction. The maximum point is reached when the rate of

change of power with respect to voltage is zero. However,

the major drawback of the conventional P&O is that, the

process is repeated periodically until the MPP is reached.

The system then oscillates about the MPP. The oscillation

can be minimized by reducing the perturbation step size.

However, a smaller perturbation size slows down the MPPT.

An improved P&O algorithm is used here as a solution to

this conflicting problem, which is shown in figure 3. Here,

instead of the same perturbation size throughout the pro-

cess, two step sizes (k1 and k2, k1 > k2) are used. The

operating voltage of the PV module is perturbed and the

resulting change in power is measured. If dP/dV is positive,

the perturbation of the operating voltage should be in the

same direction as the increment. However, if it is negative,

the system operating point is moving away from MPPT and

the operating voltage should be perturbed in the opposite

direction. Initially, when the error, i.e. E = P(n)−P(n−1)

is large the algorithm selects the step size as K = k1 to have

a fast tracking of MPP. However, at the instant when E <=10W i.e. less than 8% of the maximum power, a step size

of k2 is chosen to have a minimum oscillation at the MPP.

The exact value of k1 is chosen based on the tracking time

of MPP and it can be calculated as follows

Let, T = Maximum tracking time of MPPT controller and

Ts = Sampling time of the controller. Number of samples

(or iteration) required for the MPPT controller to reach the

MPP, Ns = T/Ts. In worst possible condition, the operating

point has to cover from 0 V to VMPP V (under STCs)

within this Ns iteration. Therefore k1 can be calculated as,

k1 =VMPP /Ns.

However, to minimize the power ripple at MPP, the step

size k2 is chosen as 1/10 times of k1

4.2 Grid synchronization controller

Synchronization between the PV inverter and the grid means

that both will have the same phase angle, frequency and

amplitude. In order to accomplish this, a 1−φ phase locked

loop (PLL) is used. It is a feedback control system which

automatically adjusts the phase of a locally generated signal

to match the phase of an input signal and hence provide a

unity power factor operation. In a grid connected PV system

the objective of the PLL is to synchronize the inverter out-

put current with the grid voltage. The schematic diagram of

the 1−φ PLL is shown in figure 4. Here the input to the PLL

structure is the grid voltage and output is its phase angle.

This phase angle is used to generate the sine wave which

acts as a reference signal to the control system. The time

required for the synchronization is dependent on the PI block

parameters, which are computed below.

From the schematic diagram it can be observed that the

error in the PI controller of the PLL structure is given by

e = Vg sin θg cos θ−Vg cos θg sin θ = Vg sin(θg−θ), (16)

where θg and θ are phase angles of the grid and the PLL

respectively.

In order to tune the parameters of PI controller, the input

to the PI controller is linearized around a working point.

Under steady state operation, the error in PI controller is zero

and the linearized error in PI controller can be expressed by

Taylor series as

f (x) ≈ f (x0) + f ′(x0).(x − x0) ⇔ sin(x)|x=0

= cos(0)(x − 0) = x. (17)

Thus, the error in PI controller becomes

ε = Vg(θg − θ). (18)

The linearized small signal transfer function of the PLL is

given by

P ll(s) =Vg

(

KP + KI

s

)1s

1 + Vg

(

KP + KI

s

)1s

=Vg

(KP

KI

)

(1 + sKI )

s2 + VgKP s + Vg

(KP

KI

) . (19)

This is a second order system with one real zero. Kp is

the proportional gain and KI is the integral gain. The natural

frequency and damping ratio can thus be stated as ωn =


√VgKP

KIand ξ =

√VgKP KI

4respectively. The relationship

between the natural frequency and the rise time for a second

order system is known to be tr ≈ 1.8ωn

[34]. The parameters

describing the PI controller can then be specified in terms of

rise time and grid voltage amplitude, KI ≈√

2ωn

≈ 0.79tr and

KP ≈ ωn

√2

Vg≈ 2.55

trVg. For a rise time of 5 ms, with optimal

damping the parameters of the PI controller equals, KP =12.75 and KI = 3.95 × 10−3.

However, if the grid frequency differs from the nominal

50 Hz, the output from the 5 ms delay block in figure 4 is

cos(

θg

)

+ A sin(

θg

)

. Assuming that a cosine trigonometric

function is used to compute the cos (θ), the error into the PI

controller becomes

Err = Vg sin(

θg − θ)

− VgA sin(

θg

)

. sin (θ) (20)

Which contains an additional AC component at (ωg + ω)

rad/ sec, which would lead to an error in PLL output, which

is the major drawback of the conventional transport delay

based PLL. A modified PLL is developed to cancel out errors

because of input frequency variation. In modified PLL, the

cosine of the PLL in feedback path is replaced by a sine

function with another 5 ms delay block. With this dual

transport delay based PLL (DTDPLL), the error into the PI

controller becomes

Err = Vg sin(

θg

)

[cos (θ) + A sin (θ)]

−Vg

[

cos(

θg

)

+ A sin(

θg

)]

. sin (θ)

= Vg sin(

θg − θ)

. (21)

From Eq. (21), it is observed that the error due to input

frequency variation is cancelled out by feedback transport

delay block. This has been validated by simulation results,

which is given in section 6.

4.3 PV inverter controller

Since the PV system is operated in both grid connected and

grid isolated mode, the controller requirement of which are

different and hence discussed separately in the following

subsections.

4.3a Grid connected mode: During grid connected mode,

the PV inverter operates as a current controlled source to

generate an output current based on reference current [35,

36]. The regulation of DC-link voltage carries the informa-

tion regarding the exchange of active power between PV mod-

ule and grid. Thus the output of DC-link controller results

Figure 4. Complete control circuit for the proposed system.


in an active current. The block diagram of DC-link voltage

controller for 1−φ two-level PV inverter is given in fig-

ure 4. Here the actual DC-link voltage of PV inverter (vdc) is

sensed and passed through a first-order low pass filter (LPF)

to eliminate the switching ripples. The difference of this fil-

tered DC-link voltage and reference DC-link voltage (v∗dc)

is given to a PI controller to regulate the DC-link voltage.

The DC-link voltage error (verr) in nth sampling instant

is given as

verr(n) = v∗dc(n) − vdc(n). (22)

The output of the PI controller at nth sampling instant is

expressed as

i∗inv(n) = i∗inv(n − 1) + KP 1(verr(n) − verr(n − 1))

+KI1verr(n). (23)

where KP 1 and KI1 are proportional and integral gains of

the DC-link voltage controller.

The output of the DC-link voltage controller gives the

peak value of the active current which is multiplied with the

grid voltage template to generate the reference current for

the PV inverter. With this control, the PV inverter can feed

the local load with a maximum current up to reference

current. If the load requirement is more than the PV gen-

eration, then the extra current is extracted from the grid.

Similarly, when the load requirement is less than the PV gen-

eration, then the surplus power is fed to the grid. These two

modes of operation are given in figure 5(a) and figure 5(b)

respectively.

In this mode, the actual inverter current is compared with

the reference current. The error is then fed to a PI con-

troller. The output of the PI controller generates a change in

the duty ratio (d) which is added to the steady state value

of the duty ratio (D) to generate a modulating signal. The

complete mathematical equation for the development of the

modulating signal is explained below.

For a two level inverter as shown in figure 1, when switch

‘1’ and ‘4’ are ON, the output voltage V0 = Vdc and when

‘2’ and ‘3’ are ON, V0 = −Vdc. Therefore, the volt-second

balance equation for the two level inverter can be written as

V0T = VdcDT + (−Vdc)(1 − D)T = 2VdcDT − VdcT .

(24)

Under steady state the duty cycle of a two level inverter can

be represented as

D = 0.5 + V0

2Vdc

. (25)

For the closed loop control under grid connected mode, V0

can be replaced by Vinv and hence the duty cycle can be

written as

D = 0.5 + Vinv

2Vdc

. (26)

The generated modulating signal during grid connected

mode can be written as

m =(

0.5 + Vinv

2Vdc

)

︸︷︷︸

D

+

(

KP + KI

s

)

(Iref − IInv)

2Vdc︸︷︷︸

d

. (27)

Figure 5. (a) During light load condition; (b) during overload condition; (c) during isolated grid operation.

Table 3. Specification of components for hardware development.

Items Specification and features

Switches Power MOSFET, IRFP460 (http://www.st.com/web/en/resource/technical/document/datasheet/CD00001584.pdf)

Isolation amplifier AD202JY (analog devices) (http://www.analog.com/en/search.html?q=ad202jy)

Current sensor TELCON HTP 50 (http://www.telcon.co.uk/PDF%20Files/HTP25.pdf)

dSPACE board DS1104 (dynafusion)

Solar power meter TM-207

Buck converter Inductor: 2 mH , capacitor: 550 μ F

Filter L: 0.2 mH, C: 100 μ F

Grid 40 V (peak),50 Hz supply grid side Inductor value:0.05 mH


Finally, the modulating signal is compared with a 3 kHz

triangular carrier signal to generate the required switching

pulses for the PV inverter to generate an inverter current,

which is equal to the reference current.

4.3b Grid isolation mode: During grid isolation mode,

the PV inverter operates as a voltage controlled source to

generate an output voltage based on reference voltage.

Similar to current controller mode, PLL is used to find the

phase angle of the grid voltage. The phase angle generated

by the PLL along with the amplitude is used to generate the

reference voltage. Although inverter is operating in isolated

mode, the PLL is necessary to ensure that whenever the grid

is reconnected, the inverter voltage is synchronized with it.

In isolated grid operation, the actual inverter output voltage

is compared with the reference voltage. The error is then

fed to a PI controller. The output of the PI controller gen-

erates a change in the duty ratio (d) which is then added to

the steady state value of the duty ratio (D) to generate the

modulating signal. The complete mathematical equation

for the development of the modulating signal in voltage-

controlled mode is given in the following equation.

m =(

0.5 + Vinv

2Vdc

)

︸︷︷︸

D

+

(

KP + KI

s

)

(Vref − VInv)

2Vdc︸︷︷︸

d

. (28)

Finally, the modulating signal is compared with a 3 kHz

triangular carrier signal to generate the required switch-

ing pulses for the inverter. The control circuit and power

flow operation under this mode are shown in figure 4 and

figure 5(c) respectively.

5. System hardware development

A prototype laboratory model for a single phase grid connec-

ted PV system is developed using specifications tabulated in

table 3 and is shown in figure 6. Various system parameters

Figure 6. Laboratory prototype model of PVDG system.

Figure 7. Simulation results of current vs. voltage characteristics of PV module. (a) Influenced by insolation but at constant temperature;

(b) influenced by temperature but at constant insolation.


Figure 8. Simulation results of power vs. voltage characteristics of PV module. (a) Influenced by insolation but at constant temperature;

(b) influenced by temperature but at constant Insolation.

(c)

(a) (b)

Figure 9. Simulation results of maximum power point tracking of PV module (a) at varying temperature; (b) varying irradiation

condition; (c) comparative analysis of conventional and modified MPPT.


like voltage and current are measured and conditioned using

Hall-effect current sensors (TELCON HTP 50) and isolation

amplifiers (AD202JY). The control algorithm is first devel-

oped in the MATLAB Simulink environment and the real

time workshop of MATLAB generates the optimized C-

code for real time implementation. The interface between

MATLAB and Digital signal processor (DSP, DS1104 of

dSPACE) allows the control algorithm to be run on the hard-

ware, which is an MPC8240 processor. Switching signals

obtained from the controller are given to the power MOS-

FETs after proper isolation and amplification. For the testing

of the complete prototype, the outputs of the DC–DC con-

verters are fed to a two-level inverter whose output is con-

nected to a resistive type local load. For the validation of grid

interfacing, a 40V (peak) (or 28.28 V (RMS)), 50 Hz grid is

prepared in the laboratory with the help of an isolation and

step down transformer.

6. Results and discussion

6.1 Simulation results

In order to verify the performance of the aforementioned

grid connected PV system, a computer-based simulation

using MATLAB Simulink is carried out. For the validation

purpose, two PV modules obtained from the manufacturer

Maharishi Solar (http://www.maharishisolar.com/) are used.

The manufacturer’s datasheet of the PV Module is given

in Appendix A. The simulation of the PV module is done

under varying irradiation (400–1000 W/m2) and temperature

(25◦C to 40◦C) conditions. The current vs. voltage char-

acteristics and power vs. voltage characteristics for these

conditions are shown in figure 7 and figure 8 respectively.

At maximum power point, the simulation results of current,

voltage and power under varying temperature and irradia-

tion conditions are presented in figure 9(a) and figure 9(b)

respectively. To show the comparative analysis between

conventional P&O based MPPT and modified MPPT, a

simulation result is given in figure 9(c). It can be observed

that the oscillation in the proposed MPPT scheme is less as

compared to the conventional P&O method.

In order to validate the efficacy of DTDPLL for frequency

other than 50 Hz input, the proposed PLL is simulated with

an input frequency of 45 Hz. Initially the input signal is

applied to the conventional PLL and after a few seconds,

the i/p signal is fed to the proposed PLL. The correspond-

ing simulation results are shown in figure 10. Figure 10(a)

shows the output phase angle of the PLL in rad/s whereas

figure 10(b) shows the i/p and o/p signal. It can be observed

that, with conventional TDPLL the error is found to be

significant when an input signal is having other than 50

Hz frequency. However, with proposed DTDPLL, the error

is almost zero and input and output signals are found to

be exactly in phase with each other. In order to show the

dynamic performance of the proposed PLL under frequency

variation, simulation results of input and output signals

under different frequency inputs are shown in figure 11.

Finally, the single-phase grid connected PV system is sim-

ulated at STCs to observe both current and voltage control of

PV Inverter. In grid connected mode, all the three switches

0.4 0.45 0.5 0.55 0.6 0.65-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

Time(s)

la

ngi

SP/

O&

P/I

I/P Signal O/P Signal

50 Hz Signal 45 Hz Signal

Figure 11. Input and output signal of proposed PLL with fre-

quency variation.

0.96 0.98 1 1.02 1.04 1.060

2

4

6

8

10

12

Time(s)

Th

eta

(ra

d/s

)

Actual Value

Reference Value

0.98 0.985 0.991

2

3

1.025 1.03 1.0351

2

3

Conventional PLL Proposed PLL

0.96 0.98 1 1.02 1.04 1.06-1

-0.5

0

0.5

1

1.5

2

2.5

3

Time(s)

I/P

& O

/P S

ign

al

Output Signal Input Signal

0.98 0.986

0.8

1

1.046 1.054

0.8

1

Conventional PLL Proposed PLL

(a) (b)

Figure 10. (a) Output phase angle; (b) input and output signal with conventional and proposed PLL when input signal frequency is of

45 Hz.


S1, S2 and S3 are closed as shown in figure 5(a) and figure

5(b). Similarly, in isolated grid operation the switches S1, S2

are closed and S3 is open. During grid connected mode, the

simulation results for both light load and overload conditions

are given in figure 12. In this mode, the DC-link voltage

controller generates the reference PV inverter current. The

reference voltage for the DC-link voltage controller is set

at 60 V and at STCs the reference current generated by the

controller is 7.4 A (RMS). It is observed from the simulation

results that, the PV inverter is able to generate the current

equal to reference current. For light load condition, a resis-

tive load of 5 � is chosen, which demands an RMS current

of 5.65 A. Therefore, the surplus PV power is fed to the

grid. During this light load condition, the grid current is out

of phase from PV inverter current and load current, which

implies that the surplus current generated by the PV inverter

is fed to the grid. Similarly, for overload conditions, a resis-

tive load of 2 � is chosen. In this case, the load requirement

is 14.14 A (RMS), which is more than the PV current (7.4

A), so the rest of the required load demand is met by the grid.

It is observed from figure 12 that during overload condition

the PV inverter current, load current and grid current are in

the same phase, which means the load requirement is ful-

filled by both PV inverter and the grid. During the transition

period from light load to overload condition, the DC-link

voltage changes from its reference value to compensate the

increase in load current. This causes a drop in capacitor

voltage, which is restored in 2–3 cycles. Similarly, during

the transition period from an overload to light load condi-

tion, the drop in load current is responded by PV inverter

with a rise in capacitor voltage, which is restored in 2–3

cycles to its reference value. The DC-link voltage controller

Figure 12. Simulation results during grid connected operation under both overload and light load condition.

Figure 13. (a) Effect of grid inductor on the voltage at PCC; (b) THD of the grid voltage.


therefore, ensures the regulation of the capacitor voltage.

The grid side inductor plays an important role during grid

connected mode. It is designed based on high frequency cur-

rent attenuation from the PV inverter to the grid. The high

value of grid inductor effect significantly on the magnitude

and %THD of voltage at PCC. This has been shown in gra-

phical form in figure 13(a) and figure 13(b) respectively.

When the switch S3 is opened, the PV inverter switches

to grid isolation mode to supply power to the local load. In

this mode, the inverter is voltage controlled to maintain 40V

(peak), 50 Hz. The voltage waveforms in this mode of oper-

ation are shown in figure 14. Initially the system is operated

under grid-connected mode at t = 0.1 s, the grid is iso-

lated from the PV inverter. In this mode of operation, the PV

inverter is operated in voltage-controlled mode to maintain

a constant voltage across the load.

6.2 Experimental results

In the first part of the experimental validation the current

vs. voltage and power vs. voltage characteristic of the PV

module are plotted based on the experimental data and are

shown in figure 15(a) and figure 15(b) respectively. For the

validation of MPPT control, the developed DC–DC buck

converter is tested on 26th June 2013 at 1:15 PM. The irra-

diation and temperature were measured as 850 W/m2 and

35◦C respectively. A resistive load was connected across

the converter and the obtained results are shown in fig-

ure 16(a). The experimental result shows the PV module

output power, current and voltage. Initially, the MPPT con-

troller was in enabled mode. The PV module output voltage;

current and power are recorded as 32 V, 2.6 A and 83 W

Figure 14. Simulation results during grid isolation mode.

respectively. After a few seconds, the MPPT controller is

disabled. Under this condition, the PV module output volt-

age; current and power are recorded as 16 V, 2.6 A and 42 W

respectively. Therefore, it is observed from figure 16(a) that

with an MPPT controller the optimal power can be extracted

from the PV module. In the second part of the experimental

validation, the PV inverter is interfaced with the grid. For the

interfacing purpose, a 1 − PLL has been used. The output

phase angle of the PLL is given in figure 16(b).Finally, the experimental results of PV system are dis-

cussed for the following two modes of operation.

Mode 1: Grid connected mode

In this mode the inverter is operated in light load and

overload conditions to obtain both steady state and transient

response.

(a) Light load condition

For the testing of prototype model under this mode, a 5

� resistive load is connected across the PV inverter. As

explained in the previous section the inverter and load volt-

age under this mode are equal to the grid voltage, which is

28.28 V (rms) or 40 V (peak). The reference current gener-

ated by DC-link voltage controller during the test condition

is 7.4 A (rms). The experimental results of PV inverter cur-

rent, load current and grid current of the system under this

mode are shown in figure 15(a). From this experimental

result, it can be observed that under light load condition, the

load requirement is less than the PV generation. Therefore

the remaining PV inverter current is fed to the grid. It can

also be observed from figure 15(a) that the inverter current,

load current are in same phase, whereas the grid current is

in opposite phase that demonstrates the surplus energy is fed

to the grid. Under this mode of operation the harmonic spec-

trum of inverter current, load current and grid current are

given in figure 16(i). The %THD for inverter current, load

current and grid current are found out to be 4.1%, 3.9% and

3.3% respectively (figure 18(i)).

(b) Over load condition

For the testing of prototype model under this mode, a 2 �

resistive load is connected across PV inverter, which acts as

a local load. The experimental results of PV inverter current,

load current and grid current of the system under current

controlled mode are shown in figure 17(b). As the load

requirement is more than the PV generation, the grid sup-

plies the rest of the load current. It can also be observed from

figure 17(b) that the inverter current, load current and grid

current are in same phase, which means that load require-

ment is met by both PV Inverter and the grid. Under this mode

of operation the harmonic spectrum of inverter current, load

current and grid current are given in figure 16(ii). The THD

for inverter current, load current and grid current are found

out to be 4.1%, 3.4% and 2.3% respectively (figure 18(ii)).


(c) Transient condition

The experimental results of PV inverter current, load cur-

rent and grid current of the PV system during the transition

period from overload to light load condition are shown

in figure 17(c). It is observed that, during the transition

period from overload to light load condition, the drop in

load current is responded by PV inverter with an increase

in capacitor voltage which is restored back to its reference

value (60V).Finally, the comparison between simulation and exper-

imental results during grid-connected mode is given in

(34.5,2.5)

0

0.5

1

1.5

2

2.5

3

0 10 20 30 40 50

Voltage (V)

Cu

rre

nt

(A)

Cu

rre

nt

(A)

Voltage (V)

(34.5,2.5)

0

0.5

1

1.5

2

2.5

3

0 10 20 30 40 50

(a) (b)

Figure 15. (a) current vs. voltage characteristics of PV module; (b) power vs. voltage characteristics of PV module from experimental

data.

Figure 16. (a) Power, current and voltage of PV module with and without MPPT controller; (b) output phase angle of PLL.

Figure 17. Inverter current, load current and grid current under (a) light load or grid feeding condition; (b) overload or load sharing

condition; (c) inverter current, load current, grid current and DC-link voltage during transition from overload to light load.

Table 4. Comparative analysis of simulated and experimental result during grid connected mode.

Light load condition Over load condition

IInv IL Ig IInv IL Ig

Simulated results 7.4 A (rms) 5.65A (rms) 1.75 A (rms) 7.4A (rms) 14.14A (rms) 6.74A (rms)

Experimental results 7.59 A (rms) 5.89A (rms) 1.75 A (rms) 7.59 A (rms) 14.38A (rms) 6.80 A (rms)


(i)

(ii)

(c)(b)(a)

(c)(b)(a)

Figure 18. Harmonic spectrum of (a) inverter current; (b) load current; (c) grid current under: (i) light load; (ii) overload condition.

Figure 19. Inverter voltage, load voltage and grid voltage under

grid connected and isolated grid operation.

table 4. From this table, it is found that simulation results arein good agreement with experimental results.

Mode 2: Grid isolation mode

For the testing of prototype model under this mode, a

20 � resistive load is connected across the PV inverter.

The inverter voltage, load voltage and grid voltage of the

proposed system under this mode are shown in figure 17.

The prototype is first operated in grid connected mode and

after some instant; the switch between PCC and grid is

opened to run the system under isolated grid mode. It is

observed from the experimental result in figure that with

the voltage control schemes the inverter and load terminal

voltage is remained constant even in isolated condition

(figure 19).

7. Conclusion

This paper has presented a complete control strategy for a

single-phase PV inverter operating in both grid connected

and grid isolated mode. For the synchronization of PV

inverter with the grid a single phase DTDPLL controller

is presented. The performance of proposed DTDPLL con-

troller is validated under varying frequency conditions. The

grid connected PV system is tested under two different

modes of operations, which are PV inverter control dur-

ing grid connected operation and grid isolation operation.

During grid connected operation, PV inverter operates in a

current controlled mode. Under this mode of operation, the

PV inverter feeds the surplus power to the grid during light

load condition, whereas during overload conditions both the

PV inverter and grid share the load requirement. During

isolated grid operation, the PV inverter operates in voltage-

controlled mode to maintain a constant voltage. For the


optimum use of PV module, a modified P&O based MPPT

controller has been used. Two 120W PV modules have been

used for the prototype development which is interfaced with

40V (peak), 50 Hz single phase grid through a PV inverter.

Finally, the developed prototype is tested under all different

conditions and is shown to work satisfactorily.

Appendix A. Datasheet of PV module.

Nomenclature

a diode ideality constant

I0 reverse saturation current

ig grid current

iinv inverter output current

iL load current

IMPP current at the MPP

IPV PV current

ISC short circuit current

ISC,ST C nominal short-circuit current

K Boltzmann constant, 1.3806503 × 10−23 J/K

KI short circuit current/temperature coefficient

KV open circuit voltage/temperature coefficient

Ns number of PV cell in series

PMAX,e maximum experimental peak output power

Q electron charge, 1.60217646 × 10−19 C

RS series resistance

RSh shunt resistance

T temperature in Kelvin

vg grid voltage

VMPP voltage at the MPP

VOC open-circuit voltage

VOC,ST C nominal open circuit voltage

Vt thermal voltage of PV module

References

[1] Blaabjerg F, Teodorescu R, Liserre M and Timbus A V 2006

Overview of control and grid synchronization for distributed

power generation systems. IEEE Trans. Ind. Electron. 53(3):

1398–1409

[2] Blaabjerg F, Zhe C and Kjaer S B 2004 Power electron-

ics as efficient interface in dispersed power generation sys-

tems. IEEE Trans. Power Electron. 19(3): 1184–1194

[3] Serban E and Serban H 2010 A control strategy for a dis-

tributed power generation microgrid application with voltage-

and current-controlled source converter. IEEE Trans. Power

Electron. 25(12): 2981–2992

[4] Chatterjee A, Keyhani A and Kapoor D 2011 Identification

of photovoltaic source models. IEEE Trans. Energy Convers.

26(3): 883–889

[5] Villalva M G, Gazoli J R and Filho E R 2009 Comprehen-

sive approach to modeling and simulation of photovoltaic

arrays. IEEE Trans. Power Electron. 24(3): 1198–1208

[6] de Brito M A G, Galotto L, Sampaio L P, de Azevedo e

Melo G and Canesin C A 2013 Evaluation of the main MPPT

techniques for photovoltaic applications. IEEE Trans. Ind.

Electron. 60(3): 1156–1167

[7] Jain S and Agarwal V 2007 Comparison of the perfor-

mance of maximum power point tracking schemes applied to

single-stage grid-connected photovoltaic systems. IET Electr.

Power Appl. 1(3): 753–762

[8] Esram T and Chapman P L 2007 Comparison of pho-

tovoltaic array maximum power point tracking tech-

niques. IEEE Trans. Energy Convers. 22(2): 439–449, doi:

10.1109/tec.2006.874230

[9] Kjaer S B 2012 Evaluation of the “Hill Climbing” and the

“Incremental Conductance” maximum power point trackers

for photovoltaic power systems. IEEE Trans. Energy Convers.

27(4): 922–929

[10] Masoum M A, Dehbonei H and Fuchs E F 2002 Theoretical

and experimental analyses of photovoltaic systems with volt-

ageand current-based maximum power-point tracking. IEEE

Trans. Energy Convers. 17(4): 514–522

[11] Alajmi B N, Ahmed K H, Finney S J and Williams B

W 2011 Fuzzy-logic-control approach of a modified hill-

climbing method for maximum power point in microgrid

standalone photovoltaic system. IEEE Trans. Power Electron.

26(4): 1022–1030

[12] Rai A K, Kaushika N, Singh B and Agarwal N 2011 Simu-

lation model of ANN based maximum power point tracking

controller for solar PV system. Sol. Energy Mater. Sol. Cells

95(2): 773–778

[13] Abdelsalam A K, Massoud A M, Ahmed S and Enjeti P 2011

High-performance adaptive perturb and observe MPPT tech-

nique for photovoltaic-based microgrids. IEEE Trans. Power

Electron. 26(4): 1010–1021

[14] Munir S and Yun Wei L 2013 Residential distribution system

harmonic compensation using PV interfacing inverter. IEEE

Trans. Smart Grid 4(2): 816–827

[15] Yi Fei W and Yun Wei L 2013 A grid fundamental and

harmonic component detection method for single-phase sys-

tems. IEEE Trans. Power Electron. 28(3): 2204–2213, http://

www.analog.com/en/search.html?q=ad202jy, http://www.tel-

con.co.uk/PDF%20Files/HTP25.pdf, http://www.st.com/web/

en/resource/technical/document/datasheet/CD00001584.pdf


[16] Busada C, Goxmez Jorge S, Leon A E and Solsona J 2012

Phase-locked loop-less current controller for grid-connected

photovoltaic systems. IET Renew. Power Generation 6(6):

400–407

[17] Feola L, Langella R and Testa A 2013 On the effects of

unbalances, harmonics and interharmonics on PLL sys-

tems. IEEE Trans. Instrum. Measur. 62(5): 2399–2409

[18] Guan-Chyun H and Hung J C 1996 Phase-locked loop tech-

niques. A survey. IEEE Trans. Ind. Electron. 43(6): 609–615,

http://www.maharishisolar.com/

[19] Monfared M, Sanatkar M and Golestan S 2012 Direct active

and reactive power control of single-phase grid-tie convert-

ers. Power Electron. IET 5(4): 1544–1550

[20] Thacker T, Boroyevich D, Burgos R and Wang F 2011 Phase-

locked loop noise reduction via phase detector implemen-

tation for single-phase systems. IEEE Trans. Ind. Electron.

58(6): 2482–2490

[21] Wang Y F and Li Y W 2011 Grid synchronization PLL based

on cascaded delayed signal cancellation. IEEE Trans. Power

Electron. 26(7): 1987–1997

[22] Carugati I, Donato P, Maestri S, Carrica D and Benedetti

M 2012 Frequency adaptive PLL for polluted single-phase

grids. IEEE Trans. Power Electron. 27(3): 2396–2404

[23] Golestan S, Monfared M, Freijedo F D and Guerrero J M

2013 Dynamics assessment of advanced single-phase PLL

structures. IEEE Trans. Ind. Electron. 60(6): 2167–2177

[24] Simon D and El-Sherief H 1995 Fuzzy logic for digital phase-

locked loop filter design. IEEE Trans. Fuzzy Syst. 3(2): 211–

218

[25] Colak I and Kabalci E 2013 Implementation of energy-

efficient inverter for renewable energy sources. Electr. Power

Components Syst. 41(1): 31–46

[26] Jiang Y, Gao F and Pan J 2010 Single-phase phase-shift full-

bridge photovoltaic inverter with integrated magnetics. Electr.

Power Components Syst. 38(7): 832–850

[27] Orabi M, Ahmed M and Abdel-Rahim O 2013 A single-

stage high boosting ratio converter for grid-connected

photovoltaic systems. Electr. Power Components Syst. 41(5):

896–911

[28] Rahim N A and Selvaraj J 2007 Hysteresis current control and

sensorless MPPT for grid-connected photovoltaic systems.

Paper presented at the IEEE International Symposium on

Industrial Electronics

[29] Kotsopoulos A, Duarte J and Hendrix M 2001 A predic-

tive control scheme for DC voltage and AC current in

grid-connected photovoltaic inverters with minimum DC link

capacitance. Paper presented at the The 27th Annual Confer-

ence of the IEEE Industrial Electronics Society

[30] Ahmed S S and Mohsin M 2011 Analytical determination

of the control parameters for a large photovoltaic generator

embedded in a grid system. IEEE Trans. Sustain. Energy 2(2):

122–130

[31] Agrawal S, Sekhar P C and Mishra S 2013 Control of single-

phase grid connected PV power plant for real as well as

reactive power feeding. Paper presented at the IEEE Inter-

national Conference on Control Applications (CCA), 28–30

August 2013

[32] Sera D, Teodorescu R and Rodriguez P 2007 PV panel model

based on datasheet values. Paper presented at the IEEE

International Symposium on Industrial Electronics

[33] Timbus A, Liserre M, Teodorescu R, Rodriguez P and

Blaabjerg F 2009 Evaluation of current controllers for

distributed power generation systems. IEEE Trans. Power

Electron. 24(3): 654–664

[34] Franklin G F, Powell J D and Emami-Naeini A 2006 Feedback

control of dynamics systems. Pretince Hall Inc

[35] Sozer Y and Torrey D A 2009 Modeling and control of util-

ity interactive inverters. IEEE Trans. Power Electron. 24(11):

2475–2483

[36] Ashari M, Keerthipala W W L and Nayar C V 2000 A

single phase parallely connected uninterruptible power sup-

ply/demand side management system. IEEE Trans. Energy

Convers. 15(1): 97–102, doi: 10.1109/60.849123

a single phase photovoltaic inverter control for grid

Documents